The ability to measure solute concentration using aspects of nonlinear acoustic propagation, given a knowledge of which solvent and solute is present, and in some cases to distinguish qualitatively among known solvent/solute systems, has already been established in the relevant literature. However, the ability to do both qualitative and quantitative measurements simultaneously and to include more than one solvent/solute system in the analysis by these techniques does not currently exist.
Propagation of sound in solvents and their solutions has long been known to be nonlinear. The nonlinearity is manifested in the generation of harmonics and in velocity-dependent dispersion. The degree of nonlinearity is a function of the intensity of the sound wave. The degree of nonlinearity is also a function of the specific, detailed interactions among solvent and solute molecules, and under some conditions can be used to identify solvents and solutes. The degree of nonlinearity is conventionally expressed as the value of the parameter B/A, where A and B are the constants in the first two terms in a perturbative power-series expansion for the nonlinear strength.
Considerable current research has been directed toward medical applications of this phenomenon as a diagnostic tool. As a simple example, diseased organs often have a different water (and solute) content from healthy organs. More sophisticated applications-oriented research addresses identification of specific organic compounds. Spatial imaging of the sources of nonlinearity has also been done and these images reveal bone, blood vessels, and muscle distinctly because of differences in nonlinearity. Nearly all of the current work in the field is being done at "physiological" sound intensities. These intensities are characteristic of conventional medical ultrasound imaging, and are sufficiently low as to preclude injury to tissues.
Since the degree of nonlinearity is itself a function of acoustic intensity, it is to be expected on general principles that higher acoustic intensities will increase the resolution of small differences among solvent/solute systems, and that higher intensities may reveal additional aspects of the nonlinear interactions between solvent and solute.
The limiting sound intensities are dictated by solution cavitation, where the solute and solvent molecules are effectively torn apart. This phenomenon is used routinely, for example, in ultrasonic cleaners, and in certain techniques to modify equilibria in chemical reactions.
Applications of nonlinear phenomena as a measurement tool are different in principle from the current generation of acoustic chemical-sensing instrumentation which uses the speed of sound and related parameters to do chemical analysis for assessment of chemical agents in artillery shells and for arms control verification purposes. Measurement of the speed of sound with sufficient accuracy to quantify the small differences between solvent/solute systems requires knowledge of a precisely-known flight path. Manufacturing tolerances among similar containers are usually found to be large enough to introduce significant ambiguity into the measurement.
Current nonlinear-propagation and speed-of-sound methods produce ambiguous results with completely unknown solutions primarily because they yield only one parameter, the nonlinear strength parameter previously mentioned, B/A, or the speed of sound, neither of which are unique to the solution. Almost any solution can be simulated to give the same speed of sound or B/A by the properties of various mixtures of different solutions.
A series of experiments have been previously performed by the present inventor to provide background information relating to measurements of changes in the speed of sound in dilute solutions as a function of the molar concentration.
The experimental apparatus used consisted of a container, a piezoelectric transducer and solution specimen in bottles. A sharp pulse of ultrasonic energy at 5 MHZ is generated by the piezoelectric transducer within the container. The container also contains three annular target rings at fixed distances from the transducer to provide pulse/echo targets which define transit time. The time-of-flight is measured by digital means as the interval between the echoes from the target rings.
The full waveform is recorded by an analog-to-digital converter. The time interval between target-ring echoes is measured with a digital phase-matching technique that has a resolution approaching 100 picoseconds.
Solutions for experiments were prepared in half-decade steps in concentration from 5.times.10.sup.-4 Molar (M) to 1.0M for NaCl, NaI, CsCl, and CsI, in two series. One series started at 1.0M, and the other at 0.5M.
The largest competing effect is that of temperature, which also changes the speed of sound in the solution. The temperature of the solutions was maintained constant at about 31.degree. C.
The time of flight as measured was an accurately linear function of concentration over almost the full range measured in all solutes as seen in FIGS. 1 and 2. These are linear plots covering more than four decades in concentration of NaCl and CsCl respectively. The time scale on the ordinate is the transit time in this particular apparatus. The zero-concentration intercept is the transit time for water.
The slope of the transit-time vs. concentration is the calibration for the solute in each case, in units of .mu.s/M for this apparatus. The slope and intercept were computed by the method of least-squares, weighted according to the experimental uncertainty at each point. Results are given in Table 1 and are plotted in FIGS. 1 and 2 for NaCl and CsCl, respectively.
TABLE 1 ______________________________________ Measured Calibration Slopes Solute Slope (.mu.s/M) ______________________________________ NaCl -6.7524 CsCl 0.1219 NaI 2.6577 CsI 25.6011 ______________________________________
The calibration for NaCl has a negative slope; the speed of sound increases as the concentration gets larger, at least up to 0.5M. The other solutes have increasingly positive calibrations. The slope for CsCl is small, but positive and easily measured with precision, as can be seen in FIG. 2.
The calibrations are shown in FIG. 3, relative to the time-of-flight for demineralized water, so that they apply to any container length.
The speed of sound in any medium is a function of the average intermolecular forces in that medium and of the mass of the individual particles involved. Solutes in a liquid change the intermolecular forces, which determine the sound speed. This work shows that, for very dilute solutions at least, the changes in intermolecular forces for a given low concentration solute are proportional to solute concentration in all cases investigated.
In a polar liquid, it can be expected that molecular or ion size, charge, hydration spheres, and similar variables also affect the intermolecular forces which control the speed of sound. Introductory texts generally state that the speed of sound is inversely proportional to the square root of the density, which is true in most cases. It is clearly not true here, however, since the density of the solution, proportional to the molecular weight in these measurements, clearly is not dominant, otherwise the calibration for NaCl could not be negative.
Consequently, the calibrations of FIG. 3 can be used directly and on-line for precise quantitative analysis of solutions of a single known solute and the difference in calibration slopes of FIG. 3 indicates that the technique can be also used for qualitative analysis as well.
Experiments in the field of solutions suggest that the nonlinearity mechanism involves hydration. Molecules in water solution can be described as being surrounded by hydration spheres of water molecules in "layers" or shells, the inner layer being most tightly bound, and other layers successively less well bound. The number and binding energy of water molecules in each layer is a function of solute molecule size, binding mechanism (e.g., electrostatic, Van Der Walls, etc.) and other parameters. The configuration and binding energies of the hydration sphere are unique properties of each solute molecule in each of its solvents, for many practical purposes at least. Liquids in general and pure solvent molecules in particular can be described as having the same structure, with each molecule being surrounded by an ordered array of other solvent molecules, the array becoming more disordered with distance, whether or not there are any solutes. Fully equivalent types of interactions affect other solvent systems, including, specifically, organic solvents.
To develop this theory of hydration and to explain the origin of nonlinear propagation, consider that an intense sound wave is propagating in a solution. During each compressive half-cycle of the sound wave, the solute, or solvent, molecule and all of its potential hydration sphere will be packed tightly together; the sound wave will be moving relatively heavy entities consisting of the solvent molecule and its hydration sphere, as it propagates. During each tensile half-cycle of the sound wave the tensile forces will strip off all or part of one or more hydration layers, depending on sound intensity, configuration, and binding energy of hydration layers. The sound wave will be moving relatively lighter entities during this part of the cycle.
Any harmonic motion in which the moving mass changes each half-cycle will generate harmonics, which is to say, is nonlinear. It is hypothesized that this is the mechanism for nonlinearity generation in solvents and their solutions.
One of the consequences of this hypothesis is that one expects the rate of nonlinearity generation with increasing intensity to change as the acoustic intensity becomes sufficient to strip all or part of each layer from the hydration sphere. Eventually the nonlinearity should stop increasing when there are no more layers to strip off, and this should happen at intensities lower than cavitation. At intermediate energies, any process which systematically changes the degree of hydration, such as complete removal of a hydration layer, will lower the rate of increase of nonlinearity with increasing acoustic intensity. Both complete and partial removal of the hydration sphere are termed "saturation" as described later.